Draw a Common Tangent to Two Equal Circles

Tangency

Definition

A tangent to a circle information technology a ttraight lino which touches the circle at i point.

Every bend ever drawn could take tangent« fatigued to it simply this affiliate is concerned simply with tangents to circles. These accept wide applications in Engineering Drawing since the outlines of most engineering details are made upwards of straight lines and arcs. Wherever a direct line meets an arc, a tangent meets a circumvolve.

Constructions

To describe a tangent to e circumvolve from any signal on the circumference (Fig. 5/1 )

ane. Depict the radius of the circle.

2. At whatever point on the circumference of a circle, the tangent and the radius are perpendicular to each other. Thus, the tangent is constitute by constructing en angle of 90* from the signal where the radius crosses the circumference.

A base geometric theorem is that the angle in a semicircle is a right angle (Fig. 5/2). This fact is made use of in many tangent constructions.

To construct a tangent from a signal P to a circle, centre O (Fig. 5/3)

two. Erect a semi -circle on 0 P to cut the circle in A.

PA produced is the required tangent (OA is the radius and is perpendicular to PA since rt is the angle in a semicircle). There are. of class, 2 tangents to the circle from P simply only one has been shown for clerity.

To conetruct a common tangent to two equal circlea (Fig. 6/4)

1. Join the centres of the two circles.

ii. From each centre, con struct lines at 90* to the centre line. The intersection of these perpendiculars with the circles gives the points of tangency.

This tangent is often descnbed at the common extenor tangent.

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To construct the common interior (or transverse or cantankerous) tangent to two equal circles, centres O

1. Join the centres 0 0,.

3. Bisect OA In B and draw a semi-circle, radius BA to cut the circle in C.

t respectively (Fig v/6)

1. Join the centres 00,.

2. Bisect 0 O, in A and draw e semi-circle, radius AO.

3. Depict a circumvolve, eye 0, radius R-r. to cut the semi-

t respectively (Fig 5/six)

ane. Join the centres 00,.

2. Bisect 0 O, in A and depict e semi-circle, radius AO.

3. Draw a circle, centre 0, radius R-r. to cut the semi-

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To construct the mutual internal tangent betwixt ii unequal circle«, centres O and O, and radii R andr respectively (Fig. 5/7)

ane. Join the centres 00,.

ii. Bisect 0 0, in A and draw a semi-circle, radius OA.

iii. Drew a circle, centre 0. radius R + r. to cut the semicircle in B.

4. Join OB. This cuts the larger circle in C.

5. Draw O.D parallel to OB. CO is the required tangent

A tangent is. by definition, a straight line. However, we do often talk of radii or curves meeting each other tengentially. We mean, of course, that the curves encounter smoothly and with no change of shape or bumps. This topic, the blending of lines and curves, is discussed in Chapter viii.

2 Fig. 2 shows a centre finder, or center foursquare in position on a 75 mm diameter bar.

Oraw, full tin. the shape of the middle finder and the piece of round bar. Show conspicuously the constructions

2 Fig. 2 shows a centre finder, or centre square in position on a 75 mm diameter bar.

Oraw, full tin can. the shape of the centre finder and the piece of round bar. Show clearly the constructions

Exercises 5 (All questions originally set in Imperial units) 1. A former in a jig for angle metal is shown in Fig 1

(a) Draw the onetime, full sue. showing in full the construction for obtaining the tangent joining the ii arcs

(b) Determine, without calculation, the centres of the four equally spaced holes to be bored in the positions indicated in the figure.

Middlesex Regional Examining Lath

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01 MENS IONS IN mm fig. 1

01 MENS IONS IN mm fig. ane

(b) the points of contact and the center for the 44 mm rad at B;

(c) the points of contact and the center for the 50 mm rad at C.

South-Cast Regional examinations Board (See Ch. viii for information not in Ch S)

Dimensions IN ■

Dimensions IN ■

3. Rg. 3 shows the outline of two pullsy wheels connected by a chugalug of negligible thickness. To a scalo of 1/10 depict the figure showing the construction necessary to obtain the points of contact of the belt and pulleys.

Middlesex Regional Examining Lath

iv. (1 ) Depict the figure ABCP shown in Fig. 4 and construct a circumvolve, centre 0. to laissez passer through the points A. 8 and C.

(2) Construct a tangent to this circumvolve touching the circle at bespeak B

(3) Construct a tangent from the bespeak P to touch the circle on the minor arc of the chord Ac.

Southern Regional Examining Board (Encounter Ch. 4 for information not in Ch. 5)

v. Fig. 5 shows a metal blank. Depict the blank, total size, showing clearly the constructions for obtaining the tangents joining the arcs.

connected by a taut belt. Draw the figure, full size, showing conspicuously the constructions for obtaining the points of contact of the chugalug and pulleys

seven. Fig. 7 shows the outline of a metal blank. Draw the bare, full size, showing conspicuously the constructions for finding exact positions of the tangents joining the arcs.

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OIMCNSIOH3 IN mm '

OIMCNSIOH3 IN mm '

8 A segment of a circle stands on a chord AB which measures 50 mm The angle in the segment is 55°. Draw the segment. Produce the chord AB to C making BC 56 mm long. From C construct a tangent to the arc of the segment.

University of London Schoolhouse Examinations (Meet Ch. 2 and Ch. 4 for information not in Ch. 5)

9. A and B are two points 100 mm apart With B as centre depict a circle 75 mm diameter. From A depict ii lines Air conditioning and AD which are tangential to the circle AC « 150 mm. From C construct another tangent to the circle to form a triangle ACD. Measure and state the lengths CD and Ad. besides bending CDA Joint Matriculation Board

10. Fig. eight shows 2 circles, A and eight. and a common external tangent and a common internal tangent. Construct (e) the given circles and tangents and (b) the smaller circle which is tangential to circle B and the two given tangents.

Measure and state the altitude between the centres of the synthetic circumvolve and circle A. Associated Examining Boa/d (Come across Ch. 4 for information non in Ch. 5)

Go along reading here: Oblique projection

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